Labour’s chief whip, Rosie Winterton, has written to reassure the party’s MPs after Jeremy Corbyn appeared to suggest at his campaign launch they could face compulsory reselection before 2020, as parliamentary boundaries are reviewed.

With more than 80% of Labour MPs refusing to back Corbyn in the recent vote of no confidence, there are fears at Westminster that some of the rebels could face reprisals if he sees off the challenge to his leadership from Pontypridd MP Owen Smith.

Asked at the formal launch of his campaign whether he could move to deselect unsupportive MPs, Corbyn pointed to the ongoing radical review of constituency boundaries, which is set to reduce the number of MPs by 50.

If the review comes into force before a general election is called, “there will be a full selection process with every constituency”, adding: “But the sitting MP will have an opportunity to put their name forward so there will be a full and open selection process for every constituency Labour party throughout the whole of the UK.”

MPs reacted angrily, with one Corbyn critic telling the Guardian many viewed it as a deliberate threat, saying, “he knew exactly what he was doing”.

His team were later forced to clarify his remarks, saying: “Jeremy does not support mandatory reselection of MPs.”

Smith, who will be the only challenger to Corbyn after his rival Angela Eagle stepped aside earlier this week, later condemned the remarks, saying: “It’s a matter for the NEC, not for the leader of the Labour party. The rules are set by the NEC.”

Corbyn struck a bullish tone at his campaign launch, at the Institute of Education in central London, making almost no mention of the leadership challenge and instead laying out plans for a future Labour government to tackle discrimination.

Asked about the polls, which show Labour lagging some way behind the Conservatives and Corbyn facing hugely negative personal ratings, the Labour leader said these would shift. “I think that once the leadership election is over, many will realise the importance of the message we are putting forwards.”

He added, to cheers from supporters: “This party is going places. This party is strong. This party is capable of winning a general election.”

He said it was “the duty and the responsibility of every Labour MP to get behind the party” and fight for “the different, fairer, kinder Britain that we can build together”.

Asked whether he agreed with comments made earlier on Thursday by his ally Diane Abbott, in which she criticised Smith for having been a “lobbyist” for the pharmaceuticals industry before he came into politics, Corbyn said he had not heard the interview.

“I hope Owen will fully agree with me that the NHS should be free at the point of use, should be run by public sector workers from the NHS, not private companies,” Corbyn said, adding that medical research should not be “farmed out” to pharmaceutical multinationals.

“I just hope – and I am sure he will – that Owen will come fully on board on the idea of our NHS being totally public,” Corbyn said.

Questions later emerged about the feasibility of the flagship policy he announced: compulsory pay audits for firms with 21 or more staff, revealing whether they are discriminating against key groups, including women, transgender people and ethnic minorities.

Some lawyers suggested the plan could potentially be illegal, because it would be possible to identify the individuals in question in small firms.

Sarah Henchoz, a partner at Allen & Overy, said: “Taken at face value, Jeremy Corbyn’s proposals would be unlawful. The principle is an extension of the current government’s gender pay gap reporting requirements but going into such a granular level of detail when it comes to employee pay and equality characteristics would likely mean that employees would be identifiable. This would be a breach of human rights and data protection law and would expose companies to legal challenge.”

However, a spokesman for Corbyn insisted the information that companies would be forced to disclose “would not be specific enough to identify individuals and would therefore not be in breach of the Data Protection Act”.

In a later interview with the BBC’s Newsnight, Corbyn rejected one of Smith’s key pledges, that a future Labour government would put the Brexit deal struck with the other 27 EU member states to the public in a second referendum.

Corbyn said: “I think you have to respect the result of the referendum, whether you welcome it or not, and respect the result which was, unfortunately, to leave”.

He rowed back from his insistence in early interviews after the referendum result was announced that article 50, the formal process for leaving the EU, should be triggered immediately. “I may not have put that as well as I should have done,” he told Newsnight. “My view was, and is, that at some point article 50 is going to be invoked – obviously, it has to be.”

David Cameron had been expected to invoke article 50 immediately after the referendum result emerged, but the new prime minister, Theresa May has insisted she will not do so until Britain has clarified what its negotiating position will be.